There are a number of applications where it is desirable to be able to identify an unknown location of an object which emits a signal. One example occurs when planning an indoor wireless local area network (LAN) having one or more RF or microwave emitters.
Of course precisely defining an object's location requires specifying coordinates in three dimensions (e.g., longitude, latitude, and altitude). In the discussion to follow, for simplicity of explanation it is assumed that the third coordinate (i.e., altitude) is either known or is otherwise easily determined once the other two coordinates (e.g., latitude and longitude) are identified. Those skilled in the art will be able to extrapolate the discussion to follow to the case where all three coordinates are to be determined.
There are a few known methods to locate signal emitters using a plurality of distributed sensors, or receivers, which are spaced apart from each other. Among these methods are: Angle of Arrival (AOA), Time of Arrival (TOA), Time Difference of Arrival (TDOA), and Received Signal Strength (RSS).
In the AOA method, the angle of arrival of the signal is measured with special directional antennas at each receiver. This information is combined to help locate the signal emitter using lines of bearing.
In the TOA method, a signal emitter transmits a signal at a predetermined or known time. Three or more sensors each measure the arrival time of the signal at that sensor. The absolute propagation time between emitter and sensor defines a distance or range. The range is computed using the well-known relation, r=vt, where r is the range, v is the propagation velocity, and t is the time of propagation between emitter and sensor. The known time of arrival at each sensor leads to circles of constant received time, centered at that sensor.
FIG. 1 illustrates some principles of a TOA method of locating an emitter 105 using three sensors 110, 120 and 130. Shown in FIG. 1 are three range-defined circles 102, 104 and 106 for the three sensors 110, 120 and 130, having respective radii r1, r2 and r3. The location where the circles 102, 104 and 106 from the three sensors 110, 120 and 130 intersect as shown in FIG. 1 is the most likely location of the signal emitter 105. In general, at least three sensors are required for the TOA method, but more than three sensors can be employed.
A chief limitation of the TOA method is that the emitter(s) to be located and the sensors must be synchronized.
The TDOA method, also known sometimes as multilateration or hyperbolic positioning, is a process of locating an emitter by accurately computing the time difference of arrival at three or more sensors of a signal emitted from an emitter to be located. In particular, if a signal is emitted from a signal emitter, it will arrive at slightly different times at two spatially separated sensor sites, the TDOA being due to the different distances to each sensor from the emitter. For given locations of the two sensors, there is a set of emitter locations that would give the same measurement of TDOA. Given two known sensor locations and a known TDOA between them, the locus of possible locations of the signal emitter lies on a hyperbola. As shown in FIG. 2A, the hyperbola is defined as the locations where the difference between distances to the two sensors is a constant, or, in this case:r1−r2=v(t1−t2).
With three or more sensors, multiple hyperbolas can be constructed from the TDOAs of different pairs of sensors. The location where the hyperbolas generated from the different sensor pairs intersect is the most likely location of the signal emitter. In practice, the sensors are time synchronized and the difference in the time of arrival of a signal from a signal emitter at a pair of sensors is measured.
FIG. 2B illustrates some principles of a TDOA method of locating an emitter 105 using three sensors 110, 120 and 130. Shown in FIG. 2 are three range-defined hyperbolas 202, 204 and 206 for the three sensor pairs 110/120, 110/130 and 120/130. The location where the hyperbolas 202, 204 and 206 from the three sensor pairs intersect, as shown in FIG. 2B, is the most likely location of the signal emitter 105. In general, at least three sensors are required for the TDOA method, but more than three sensors can be employed.
In many cases, the time-difference of arrival of a signal at two sensors is difficult to measure since the timing and signal characteristics of the emitter are unknown. In those cases, cross-correlation is a common method for determining the delay τ. FIG. 3 shows an example cross-correlation curve 310. The time-difference of arrival between the two sensors is defined as the location 312 where the curve 310 has its maximum.
In the RSS method, the power of the received signal at each sensor is measured, and the signal strength information is processed to help locate the signal emitter. There are a few different emitter location procedures that employ RSS.
In a basic RSS procedure, the power of the signal received at each sensor is measured. By knowing the broadcast power of the emitter, P0, one can convert the received power level, P1, to a range using the idealized expression: P1=P0*r1−2. Other variants of this equation use statistical approaches to account for varieties in terrain. The range from each sensor defines a circle of probable locations for the emitter, centered at that receiver, similar to what is shown in FIG. 1.
Another form of RSS is a relative power measurement, used when the power level of the signal transmitted at the emitter is not known. In this approach the relative signal power is measured at a pair of two sensors, and the received power levels at the sensors are processed to determine a circle of probable locations for the emitter.
A more detailed explanation of principles employed in such an RSS method of locating a signal emitter will now be provided with respect to FIG. 4.
FIG. 4 illustrates a general case of an emitter 105 and two sensors 110 and 120 which each receives a signal from emitter 105 wherein a circle 402 of probable locations for emitter 105 is determined from a ratio the received signal powers at sensors 110 and 120.
In free space, the received power of a signal transmitted by emitter 105 decreases with the square of the distance from emitter 105.
                                          P            1                    =                                                    P                0                            ⁡                              (                                                      r                    0                                                        r                    1                                                  )                                      2                          ,                            (        1        )            where r1 is the distance between emitter 105 and first sensor 110, and 2 is the exponential rate at which the power decreases with distance.
Likewise the received power P2 at second sensor 120 is:
                                          P            2                    =                                                    P                0                            ⁡                              (                                                      r                    0                                                        r                    2                                                  )                                      2                          ,                            (        2        )            where r2 is the distance between emitter 105 and second sensor 120.
This leads to:
                                          P            1                                P            2                          =                              (                                          r                2                                            r                1                                      )                    2                                    (        3        )            
With a bit of manipulation this yields:
                                                        log              ⁡                              (                                  P                  1                                )                                      -                          log              ⁡                              (                                  P                  2                                )                                              2                =                                            r              2                                      r              1                                =                      const            =            α                                              (        4        )            
This method is sometimes referred to as Signal Attenuation Difference of Arrival (SADOA). It can be shown that this leads to the circle 402 (the so-called circle of Apollonius) of a given radius R and centered on a point X0, Y0 located on the line 401 defined by the two sensors 110 and 120. This relationship is illustrated in FIG. 4.
With at least three sensors (e.g., A, B & C), three such circles are generated from the corresponding three unique pairs of sensors (e.g., A/B, A/C & B/C), and the location of emitter 100 can be found where the three circles intercept.
However, the addition of measurement uncertainty and noise makes it difficult to locate a sensor analytically with a high degree of accuracy using the AOA, TOA, TDOA, and RSS techniques as described above. Several error factors affect the accuracy of measurements made by the sensors. These error factors may include:                Noise. In low Signal-to-noise ratio (SNR) situations, emitter location is more difficult to determine with a high degree of accuracy because measurements of signal power, time-of-arrival, etc. are affected.        Timing and calibration errors. Although these errors are typically small compared to other errors described here, there is nevertheless a need for algorithms that are robust in instances where these errors are significant.        Competing emitters. Signals from multiple emitters can lead to ambiguous results.        Multipath propagation. Reflections from multipath propagation can distort or obscure the true time of arrival, angle of arrival, or strength of a signal received at a sensor.        Blocked line-of-sight, or un-detected direct path (UDP), is a condition in which the main propagation path between the emitter and receiver is blocked.        
Some or all of these errors can affect the graphical depictions in FIGS. 1 & 2, causing the circles or hyperbolas to move so that they do not all intersect at a single point.
The effect of all of these errors is illustrated in the example shown in FIG. 5.
FIG. 5 illustrates a TOA method of locating an emitter 105 using three sensors 110, 120 and 130 in the presence of one or more of the factors listed above. Shown in FIG. 5 are three range-defined circles 502, 504 and 506 for the three sensors 110, 120 and 130, having respective radii r1, r2 and r3. Because of measurement uncertainty due to one or more of the error-generating factors described above, the three circles 502, 504 and 506 do not intersect at one point. Instead, the three circles define an overlap region 505 which may be considered a most likely region for the location of emitter 105. It can be understood that as the measurement uncertainty increases due to various factors described above, the size of the overlap region 505 may increase to such a degree that the emitter's location cannot be determined to a desired level of accuracy.
Thus, more robust methods of locating an emitter are required to obtain a more accurate solution.
What is needed, therefore, is a method and system for locating signal emitters that addresses one or more of these shortcomings.